Finite element modeling of multiscale transport phenomena:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2011
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | xiii, 250 p. ill. 24 cm |
| ISBN: | 9781848164291 1848164297 |
Internformat
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| 245 | 1 | 0 | |a Finite element modeling of multiscale transport phenomena |c Vahid Nassehi ; Mahmoud Parvazini |
| 264 | 1 | |a London |b Imperial College Press |c 2011 | |
| 300 | |a xiii, 250 p. |b ill. |c 24 cm | ||
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| 650 | 4 | |a Transport theory / Mathematical models | |
| 650 | 4 | |a Multiscale modeling | |
| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804145644742377472 |
|---|---|
| adam_text | Titel: Finite element modeling of multiscale transport phenomena
Autor: Nassehi, Vahid
Jahr: 2011
Contents
1. Weighted Residual Finite Element Method 1
1.1 Basic Concept.......................... 1
1.1.1 Practical procedure................... 2
1.1.2 Finite element approximations............ 4
1.2 Numerical Integration..................... 6
1.2.1 Mapping of irregulär and curved elements onto
master elements .................... 7
1.3 Steps Used to Obtain a Finite Element Solution
for a Field Problem....................... 13
1.3.1 Example 1........................ 15
1.3.2 Example 2........................ 21
References............................... 27
2. Shape Functions and Fundamental Properties
of Finite Elements 29
2.1 Interpolation Polynomials................... 30
2.2 Shape Functions of Simplex Elements ............ 31
2.2.1 One-dimensional linear element............ 31
2.2.2 Two-dimensional simplex element........... 32
2.2.3 Three-dimensional simplex element.......... 35
2.3 Some Examples of Complex and Multiplex Elements .... 37
2.3.1 Quadratic and cubic one-dimensional elements ... 37
2.3.2 Four-node two-dimensional element.......... 40
2.4 Convergence of Finite Element Approximations....... 42
2.5 Continuity Conditions..................... 44
2.6 Solved Examples........................ 44
2.6.1 Example 1: Limitation of the Standard Galerkin
procedure........................ 44
x Finite Element Modeling of Multiscale Transport Phenomena
2.6.2 Example 2: A further problem associated with the
use of the Standard Galerkin finite element method . 48
2.6.3 Bubble function enriched elements.......... 51
References............................... 53
3. Basic Concepts of Multiscale Finite Element Modeling 55
3.1 Stabilization of Finite Element Schemes........... 55
3.1.1 Upwinded finite element schemes........... 56
3.1.2 Upwinding techniques................. 57
3.2 Multiscale Approach...................... 59
3.2.1 Variational multiscale method............. 60
3.2.2 (RFB) function method................ 62
3.3 Practical Implementation of the RFB Function Method . . 64
3.3.1 Multiscale finite element Solution of the DR equation
using RFB function method.............. 65
3.3.2 Multiscale finite element Solution of the CD
equation using RFB function method ........ 87
3.3.3 Multiscale finite element Solution of the CDR
equation using RFB function method ........ 94
3.4 Practical Implementation of the STC Method........ 106
3.4.1 Multiscale finite element Solution of the DR equation
using STC method................... 108
3.4.2 Multiscale finite element Solution of the CD equation
using STC method................... 113
3.4.3 Multiscale finite element Solution of the CDR
equation using STC method.............. 118
References............................... 122
4. Simulation of Multiscale Transport Phenomena
in Multidimensional Domains 125
4.1 Two-dimensional Multiscale Finite
Element Technique....................... 125
4.2 Selection of Bubble Functions and Calculation
of Bubble Coefficients..................... 129
4.3 RFB Functions Corresponding
to the Two-Dimensional DR Equation............ 131
4.3.1 Derivation of polynomial bubble function coefficients
for the DR equation using the STC method..... 133
4.3.2 Elimination of the boundary integrals........ 133
Contents xi
4.3.3 Solution of a benchmark two-dimensional
DR problem....................... 134
4.4 Solution of Two-Dimensional Convection-Diffusion
(CD) Equation......................... 140
4.4.1 Governing CD equation and boundary conditions . . 140
4.4.2 RFB functions corresponding
to the two-dimensional CD equation......... 141
4.4.3 Two-dimensional bubble functions
for bilinear elements.................. 141
4.4.4 Elimination of the boundary integrals........ 142
4.4.5 Solution of a benchmark two-dimensional
CD problem....................... 143
4.5 Solution of Convection-Diffusion-Reaction
(CDR) Problems........................ 143
4.5.1 Governing CDR equation and boundary
conditions........................ 144
4.5.2 Derivation of RFB functions for the CDR
equation......................... 146
4.5.3 Solution of a benchmark two-dimensional
CDR equation ..................... 146
4.6 Solution of Transport Equations Using Bubble
Function-Enriched Triangulär Elements ........... 149
4.7 Multiscale Finite Element Methods
for Time-Dependent Problems................. 152
4.7.1 Multiscale space?time finite element
discretization...................... 153
4.7.2 Multiscale space?time finite element modeling .... 154
4.7.3 Two-dimensional space-time bubble functions
for enrichment of bilinear elements.......... 155
4.7.4 Elimination of the boundary integrals........ 156
4.7.5 Transient CD problem................. 156
References............................... 158
5. Application of Multiscale Finite Element
Schemes to Fluid Flow Problems 161
5.1 Two-Dimensional and Axisymmetric Flow Regimes ?
Governing Equations...................... 161
Finite Element Modeling of Multiscale Transport Phenomena
5.2 Modeling of Isothermal Brinkman Flow of a Newtonian Fluid
in a Two-Dimensional Domain Using Multiscale Finite
Element Schemes........................ 164
5.2.1 Continuous penalty scheme.............. 167
5.2.2 Bubble-enriched shape functions used in conjunction
with the continuous penalty method......... 172
5.2.3 Solved example ? unidirectional flow........ 172
5.3 Solution of the Energy Equation............... 174
5.3.1 Finite element scheme used to solve
the energy equation.................. 175
5.3.2 Bubble-enriched shape functions used in the Solution
of the energy equation................. 176
5.3.3 Solved example ? Non-isothermal
unidirectional flow................... 176
5.3.4 Higher-order elements and mesh refinement..... 179
5.4 Multidirectional, Nonisothermal Porous Flow........ 180
5.5 Inclusion of Inertia Effects in Porous Flow Models..... 181
5.5.1 Derivation of bubble functions for Brinkman-Hazen-
Dupuit-Darcy equation................ 184
5.5.2 Solved example ? High velocity unidirectional
porous flow....................... 184
5.5.3 Solved example ? Multidirectional, high-velocity
porous flow....................... 185
5.6 Solution of Axisymmetric Brinkman Equation........ 185
5.6.1 Derivation of the continuous penalty finite element
scheme for axisymmetric Brinkman equation .... 188
5.6.2 Derivation of bubble functions for axisymmetric
Brinkman equation................... 189
References............................... 191
Computer Program 193
6.1 Program Structure....................... 193
6.2 Source Code........................... 194
6.3 Input File Structure...................... 220
6.4 Output Files .......................... 225
6.4.1 DR equation?dissipation case............ 225
6.4.2 DR equation?production case............ 228
Contents xiii
6.4.3 CD equation...................... 230
6.4.4 CDR equation ..................... 233
Appendices 237
Author Index 245
Subject Index 247
|
| any_adam_object | 1 |
| author | Nassehi, Vahid Parvazinia, Mahmoud |
| author_facet | Nassehi, Vahid Parvazinia, Mahmoud |
| author_role | aut aut |
| author_sort | Nassehi, Vahid |
| author_variant | v n vn m p mp |
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| bvnumber | BV037365730 |
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| dewey-full | 530.15825 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15825 |
| dewey-search | 530.15825 |
| dewey-sort | 3530.15825 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| isbn | 9781848164291 1848164297 |
| language | English |
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| spelling | Nassehi, Vahid Verfasser aut Finite element modeling of multiscale transport phenomena Vahid Nassehi ; Mahmoud Parvazini London Imperial College Press 2011 xiii, 250 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and indexes Finite element method Transport theory / Mathematical models Multiscale modeling Mathematisches Modell Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Transportprozess (DE-588)4185932-7 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 gnd rswk-swf Finite-Elemente-Methode (DE-588)4017233-8 s Transportprozess (DE-588)4185932-7 s DE-604 Strömungsmechanik (DE-588)4077970-1 s Parvazinia, Mahmoud Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022519185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nassehi, Vahid Parvazinia, Mahmoud Finite element modeling of multiscale transport phenomena Finite element method Transport theory / Mathematical models Multiscale modeling Mathematisches Modell Strömungsmechanik (DE-588)4077970-1 gnd Transportprozess (DE-588)4185932-7 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4185932-7 (DE-588)4017233-8 |
| title | Finite element modeling of multiscale transport phenomena |
| title_auth | Finite element modeling of multiscale transport phenomena |
| title_exact_search | Finite element modeling of multiscale transport phenomena |
| title_full | Finite element modeling of multiscale transport phenomena Vahid Nassehi ; Mahmoud Parvazini |
| title_fullStr | Finite element modeling of multiscale transport phenomena Vahid Nassehi ; Mahmoud Parvazini |
| title_full_unstemmed | Finite element modeling of multiscale transport phenomena Vahid Nassehi ; Mahmoud Parvazini |
| title_short | Finite element modeling of multiscale transport phenomena |
| title_sort | finite element modeling of multiscale transport phenomena |
| topic | Finite element method Transport theory / Mathematical models Multiscale modeling Mathematisches Modell Strömungsmechanik (DE-588)4077970-1 gnd Transportprozess (DE-588)4185932-7 gnd Finite-Elemente-Methode (DE-588)4017233-8 gnd |
| topic_facet | Finite element method Transport theory / Mathematical models Multiscale modeling Mathematisches Modell Strömungsmechanik Transportprozess Finite-Elemente-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022519185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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